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系统非对称性及记忆性对布朗马达输运行为的影响

王飞 谢天婷 邓翠 罗懋康

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Citation:

系统非对称性及记忆性对布朗马达输运行为的影响

王飞, 谢天婷, 邓翠, 罗懋康

Influences of the system symmetry and memory on the transport behavior of Brownian motor

Wang Fei, Xie Tian-Ting, Deng Cui, Luo Mao-Kang
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  • 在对分数阶布朗马达输运现象研究的基础上,引入了描述系统势场对称性的参数(简称对称性参数),并详细分析了该参数及记忆性参数(分数阶阶数)对粒子输运状态的影响. 仿真结果表明,分数阶阶数和对称性参数的共同作用会使得布朗粒子形成定向输运反向流,反向后达到最大平均流速所对应的阶数与外加驱动力频率无关联,但会随对称性参数的增加而单调递增.
    Based on the research on transport phenomenon of fractional Brownian motor, a systematic parameter (i.e. symmetry parameter) which describes the asymmetry of the periodic potential field is introduced, and the influences of the symmetry parameter and the memory parameter (i.e. the fractional order) on the transport behavior are also investigated. The numerical results show that the combined effect of fractional order and symmetry parameter can result in the reverse flow of Brownian particle's transport, and the fractional order corresponding to the maximal averaged velocity is irrelevant to the frequency of the external periodic force, but it will still increase monotonically as the symmetry parameter increases.
    • 基金项目: 国家自然科学基金(批准号:11171238)和电子信息控制重点实验室基金(批准号:2013035)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11171238) and the Foundation of Science and Technology on Electronic Information Control Laboratory, China (Grant No. 2013035).
    [1]

    Hänggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 387

    [2]

    Smoluchowski M V 1912 Physik. Z. 13 1069

    [3]

    Feynman R P, Leighton R B, Sands M 1963 The Feynman Lectures on Physics (Boston: Addison-Wesley) p46

    [4]

    Fendrik A J, Romanelli L 2012 Phys. Rev. E 85 041149

    [5]

    Zheng Z G 2004 Spatiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) pp279-286 (in Chinese) [郑志刚 2004 耦合非线性系统的时空动力学与合作行为 (北京: 高等教育出版社) 第279–286页]

    [6]

    Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810

    [7]

    Astumian R, Bier M 1994 Phys. Rev. Lett. 72 1766

    [8]

    Reimann P 2002 Phys. Rep. 361 57

    [9]

    Ai B Q, He Y F, Zhong W R 2010 Phys. Rev. E 82 061102

    [10]

    Yang M C, Ripoll M 2013 Phys. Rev. E 87 062110

    [11]

    Simon M S, Sancho J M, Lindenberg K 2013 Phys. Rev. E 88 062105

    [12]

    Gao T F, Zheng Z G, Chen J C 2013 Chin. Phys. B 22 080502

    [13]

    Bhat D, Gopalakrishnan M 2013 Phys. Rev. E 88 042702

    [14]

    Liu F, Anh V V, Turner I, Zhuang P 2003 J. Appl. Math. Comput. 13 233

    [15]

    Zhang L, Deng K, Luo M K 2012 Chin. Phys. B 21 090505

    [16]

    Goychuk I, Kharchenko V 2012 Phys. Rev. E 85 051131

    [17]

    Ernst D, Hellmann M, Kohler J, Weiss M 2012 Soft Matter 8 4886

    [18]

    Wang F, Deng C, Tu Z, Ma H 2013 Acta Phys. Sin. 62 040501 (in Chinese) [王飞, 邓翠, 屠浙, 马洪 2013 物理学报 62 040501]

    [19]

    Oldham K B, Spanier J 1974 The Fractional Calculus (New York: Academic Press) pp198-216

    [20]

    Kou S C, Xie X S 2004 Phys. Rev. Lett. 93 180603

    [21]

    Gao S L, Zhong S C, Wei K, Ma H 2012 Acta Phys. Sin. 61 100502 (in Chinese) [高仕龙, 钟苏川, 韦鹍, 马洪 2012 物理学报 61 100502]

    [22]

    Podlubny I 1999 Fractional Differential Equations (San Diego: Academic Press) pp78-81

    [23]

    Samko S G, Kilbas A A, Marichev O I 1993 Fractional Integrals and Derivatives Theory and Applications (New York: Gordon and Breach Science Publisher Inc.) pp321-344

    [24]

    He Y F, Ai B Q 2010 Phys. Rev. E 81 021110

    [25]

    Bai W S M, Peng H, Tu Z, Ma H 2012 Acta Phys. Sin. 61 210501 (in Chinese) [白文斯密, 彭皓, 屠浙, 马洪 2012 物理学报 61 210501]

  • [1]

    Hänggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 387

    [2]

    Smoluchowski M V 1912 Physik. Z. 13 1069

    [3]

    Feynman R P, Leighton R B, Sands M 1963 The Feynman Lectures on Physics (Boston: Addison-Wesley) p46

    [4]

    Fendrik A J, Romanelli L 2012 Phys. Rev. E 85 041149

    [5]

    Zheng Z G 2004 Spatiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) pp279-286 (in Chinese) [郑志刚 2004 耦合非线性系统的时空动力学与合作行为 (北京: 高等教育出版社) 第279–286页]

    [6]

    Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810

    [7]

    Astumian R, Bier M 1994 Phys. Rev. Lett. 72 1766

    [8]

    Reimann P 2002 Phys. Rep. 361 57

    [9]

    Ai B Q, He Y F, Zhong W R 2010 Phys. Rev. E 82 061102

    [10]

    Yang M C, Ripoll M 2013 Phys. Rev. E 87 062110

    [11]

    Simon M S, Sancho J M, Lindenberg K 2013 Phys. Rev. E 88 062105

    [12]

    Gao T F, Zheng Z G, Chen J C 2013 Chin. Phys. B 22 080502

    [13]

    Bhat D, Gopalakrishnan M 2013 Phys. Rev. E 88 042702

    [14]

    Liu F, Anh V V, Turner I, Zhuang P 2003 J. Appl. Math. Comput. 13 233

    [15]

    Zhang L, Deng K, Luo M K 2012 Chin. Phys. B 21 090505

    [16]

    Goychuk I, Kharchenko V 2012 Phys. Rev. E 85 051131

    [17]

    Ernst D, Hellmann M, Kohler J, Weiss M 2012 Soft Matter 8 4886

    [18]

    Wang F, Deng C, Tu Z, Ma H 2013 Acta Phys. Sin. 62 040501 (in Chinese) [王飞, 邓翠, 屠浙, 马洪 2013 物理学报 62 040501]

    [19]

    Oldham K B, Spanier J 1974 The Fractional Calculus (New York: Academic Press) pp198-216

    [20]

    Kou S C, Xie X S 2004 Phys. Rev. Lett. 93 180603

    [21]

    Gao S L, Zhong S C, Wei K, Ma H 2012 Acta Phys. Sin. 61 100502 (in Chinese) [高仕龙, 钟苏川, 韦鹍, 马洪 2012 物理学报 61 100502]

    [22]

    Podlubny I 1999 Fractional Differential Equations (San Diego: Academic Press) pp78-81

    [23]

    Samko S G, Kilbas A A, Marichev O I 1993 Fractional Integrals and Derivatives Theory and Applications (New York: Gordon and Breach Science Publisher Inc.) pp321-344

    [24]

    He Y F, Ai B Q 2010 Phys. Rev. E 81 021110

    [25]

    Bai W S M, Peng H, Tu Z, Ma H 2012 Acta Phys. Sin. 61 210501 (in Chinese) [白文斯密, 彭皓, 屠浙, 马洪 2012 物理学报 61 210501]

计量
  • 文章访问数:  2322
  • PDF下载量:  507
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-03-21
  • 修回日期:  2014-04-28
  • 刊出日期:  2014-08-05

系统非对称性及记忆性对布朗马达输运行为的影响

  • 1. 四川大学数学学院, 成都 610065;
  • 2. 电子信息控制重点实验室, 成都 610036;
  • 3. 西南技术物理研究所, 成都 610041
    基金项目: 

    国家自然科学基金(批准号:11171238)和电子信息控制重点实验室基金(批准号:2013035)资助的课题.

摘要: 在对分数阶布朗马达输运现象研究的基础上,引入了描述系统势场对称性的参数(简称对称性参数),并详细分析了该参数及记忆性参数(分数阶阶数)对粒子输运状态的影响. 仿真结果表明,分数阶阶数和对称性参数的共同作用会使得布朗粒子形成定向输运反向流,反向后达到最大平均流速所对应的阶数与外加驱动力频率无关联,但会随对称性参数的增加而单调递增.

English Abstract

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